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Time Limit: 2 sec / Memory Limit: 1024 MB

制約

• 1\leq N \leq 2 \times 10^5
• 1\leq A_i,B_i \leq N
• A,B はそれぞれ昇順にソートされている。
• 入力はすべて整数

入力

N
A_1 A_2 \cdots A_N
B_1 B_2 \cdots B_N


入力例 1

6
1 1 1 2 2 3
1 1 1 2 2 3


出力例 1

Yes
2 2 3 1 1 1


入力例 2

3
1 1 2
1 1 3


出力例 2

No


入力例 3

4
1 1 2 3
1 2 3 3


出力例 3

Yes
3 3 1 2


Score : 600 points

Problem Statement

Given are two sequences A and B, both of length N. A and B are each sorted in the ascending order. Check if it is possible to reorder the terms of B so that for each i (1 \leq i \leq N) A_i \neq B_i holds, and if it is possible, output any of the reorderings that achieve it.

Constraints

• 1\leq N \leq 2 \times 10^5
• 1\leq A_i,B_i \leq N
• A and B are each sorted in the ascending order.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_N
B_1 B_2 \cdots B_N


Output

If there exist no reorderings that satisfy the condition, print No.

If there exists a reordering that satisfies the condition, print Yes on the first line. After that, print a reordering of B on the second line, separating terms with a whitespace.

If there are multiple reorderings that satisfy the condition, you can print any of them.

Sample Input 1

6
1 1 1 2 2 3
1 1 1 2 2 3


Sample Output 1

Yes
2 2 3 1 1 1


Sample Input 2

3
1 1 2
1 1 3


Sample Output 2

No


Sample Input 3

4
1 1 2 3
1 2 3 3


Sample Output 3

Yes
3 3 1 2